Salespeople of a large sales force received an annual bonus based upon performance. The size of the bonuses was normally distributed with a mean of £1000 and a standard deviation of £400.
The salary of the salespeople was normally distributed, too. The salaries yearly had mean £35,000 and standard deviation of £8,000.
Assume that salary and bonus sizes are independent.
a. Find the distribution of the annual income (salary and bonus) of salespeople in this company. Report its expected value, variance, and standard deviation. Please submit your calculations.
b. What is the probability that the yearly income of a salesman is larger than £55,000? Please solve this section using Excel and submit the formula you used, an explanation, and the answer.